Public facility location using dispersion, population, and equity criteria

From a practical perspective, the paper demonstrates that the appropriate use of dispersion, population, and equity criteria can lead to fairly good solutions with respect to the p-median objective. The only stipulation is that the decision maker verifies (through simple constraint checks) that the chosen locations meet the dispersion, population, and equity criteria. An empirical investigation is conducted to obtain appropriate values for these parameters. From a location science perspective, a new location model that accounts for equity and efficiency simultaneously is studied and analyzed. Specifically, the p-maxian problem with side constraints on dispersion, population, and equity is developed, its NP-completeness established, and valid inequalities and bounds derived. Computational tests show encouraging results.

[1]  Mark A. Turnquist,et al.  Pre-positioning of Emergency Supplies for Disaster Response , 2006, 2006 IEEE International Symposium on Technology and Society.

[2]  A. Mehrez,et al.  On the Implementation of Quantitative Facility Location Models: The Case of a Hospital in a Rural Region , 1996 .

[3]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[4]  Rajan Batta,et al.  The Maximal Expected Covering Location Problem: Revisited , 1989, Transp. Sci..

[5]  RICHARD C. LARSON,et al.  A hypercube queuing model for facility location and redistricting in urban emergency services , 1974, Comput. Oper. Res..

[6]  Richard C. Larson,et al.  On Insensitivities in Urban Redistricting and Facility Location , 1972, Oper. Res..

[7]  Rajan Batta,et al.  Optimization of aeromedical base locations in New Mexico using a model that considers crash nodes and paths. , 2008, Accident; analysis and prevention.

[8]  Timothy J. Lowe,et al.  Demand Point Aggregation for Location Models , 2002 .

[9]  R. Garfinkel,et al.  Locating an Obnoxious Facility on a Network , 1978 .

[10]  Horst A. Eiselt,et al.  Location analysis: A synthesis and survey , 2005, Eur. J. Oper. Res..

[11]  Alan T. Murray,et al.  IMPACT MODELS FOR SITING UNDESIRABLE FACILITIES , 2005 .

[12]  By Zorica Nedovic̀-Budic̀ Geographic Information Science Implications for Urban and Regional Planning , 2000 .

[13]  Nasrin Asgari,et al.  Multiple criteria facility location problems: A survey , 2010 .

[14]  Stefanie Seiler,et al.  Facility Layout And Location An Analytical Approach , 2016 .

[15]  Rajan Batta,et al.  Locating an Ambulance on the Amherst Campus of the State University of New York at Buffalo , 1990 .

[16]  Richard L. Church,et al.  SYMPOSIUM ON LOCATION PROBLEMS: IN MEMORY OF LEON COOPER , 1984 .

[17]  Jörg Fliege,et al.  Some personal views on the current state and the future of locational analysis , 1998 .

[18]  R. Church,et al.  Location Modeling Utilizing Maximum Service Distance Criteria , 2010 .

[19]  C. Revelle,et al.  Heuristic concentration: Two stage solution construction , 1997 .

[20]  Mark S. Daskin,et al.  What you should know about location modeling , 2008 .

[21]  Timothy J. Lowe,et al.  Distance Constraints for Tree Network Multifacility Location Problems , 1978, Oper. Res..

[22]  António P. Antunes,et al.  Location Analysis Helps Manage Solid Waste in Central Portugal , 1999, Interfaces.

[23]  W. L. Price,et al.  Locating a Blood Bank , 1986 .

[24]  Pierre Hansen,et al.  Dispersing Facilities on a Network , 1995 .

[25]  Vladimir Marianov,et al.  New Trends in Public Facility Location Modeling , 2004 .

[26]  Erhan Erkut,et al.  Analytical models for locating undesirable facilities , 1989 .

[27]  David J. Eaton,et al.  Determining Emergency Medical Service Vehicle Deployment in Austin, Texas , 1985 .

[28]  Erhan Erkut,et al.  The discrete p-Maxian location problem , 1990, Comput. Oper. Res..

[29]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[30]  Horst W. Hamacher,et al.  The Continuous Stop Location Problem in Public Transportation Networks , 2009, Asia Pac. J. Oper. Res..

[31]  Timothy J. Lowe,et al.  Convex Location Problems on Tree Networks , 1976, Oper. Res..

[32]  Charles ReVelle,et al.  The Theory of Welfare Considerations in Public Facility Location Problems , 2010 .

[33]  Rajan Batta,et al.  On the accuracy of demand point solutions to the planar, manhattan metric, p-median problem, with and without barriers to travel , 1988, Comput. Oper. Res..

[34]  M. Brandeau,et al.  An overview of representative problems in location research , 1989 .

[35]  Julie M. Minde Building a Framework for a Spatial Decision Support System for Co-locating Public Facilities , 2009 .

[36]  M. Kuby Programming Models for Facility Dispersion: The p‐Dispersion and Maxisum Dispersion Problems , 2010 .

[37]  I. Moon,et al.  An Analysis of Network Location Problems with Distance Constraints , 1984 .

[38]  M. Kuby,et al.  Dispersion of Nodes Added to a Network , 2005 .

[39]  Oded Berman,et al.  Optimal Server Location on a Network Operating as an M/G/1 Queue , 1985, Oper. Res..

[40]  Oded Berman,et al.  The Stochastic Queue p-Median Problem , 1987, Transp. Sci..

[41]  Mengjie Han,et al.  Does Euclidean distance work well when the p-median model is applied in rural areas? , 2012, Ann. Oper. Res..

[42]  Robert F. Love,et al.  AN EMPIRICAL COMPARISON OF BLOCK AND ROUND NORMS FOR MODELLING ACTUAL DISTANCES. , 1994 .

[43]  Mark L. Burkey,et al.  A Location-based Comparison of Health Care Services in Four U.S. States with Efficiency and Equity , 2012 .

[44]  Arie Tamir,et al.  Obnoxious Facility Location on Graphs , 1991, SIAM J. Discret. Math..

[45]  R. L. Francis,et al.  A Multimedian Problem with Interdistance Constraints , 1988 .

[46]  Charles ReVelle,et al.  Optimal location under time or distance constraints , 1972 .

[47]  Erhan Erkut,et al.  Distance-constrained multifacility minimax location problems on tree networks , 1992, Networks.

[48]  Richard C. Larson,et al.  Urban Operations Research , 1981 .

[49]  M. John Hodgson,et al.  Heuristic concentration for the p-median: an example demonstrating how and why it works , 2002, Comput. Oper. Res..

[50]  Oded Berman,et al.  The minimum weighted covering location problem with distance constraints , 2008, Comput. Oper. Res..

[51]  Trevor S. Hale,et al.  Location Science Research: A Review , 2003, Ann. Oper. Res..

[52]  Mark S. Daskin,et al.  Strategic facility location: A review , 1998, Eur. J. Oper. Res..

[53]  Donald M. McAllister Equity and Efficiency in Public Facility Location , 2010 .

[54]  S. S. Ting,et al.  A Linear-Time Algorithm for Maxisum Facility Location on Tree Networks , 1984, Transp. Sci..

[55]  Edward Minieka,et al.  Anticenters and antimedians of a network , 1983, Networks.

[56]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[57]  Yukun Cheng,et al.  The p-maxian problem on interval graphs , 2010, Discret. Appl. Math..